<html>
 <head>
  <meta charset="utf-8"/>
  <meta content="width=device-width, initial-scale=1, maximum-scale=1, user-scalable=no" name="viewport"/>
  <title>
   easttiger的回复  | 数螺 | NAUT IDEA
  </title>
  <link href="http://cdn.bootcss.com/bootstrap/3.3.6/css/bootstrap-theme.min.css" rel="stylesheet"/>
  <link href="http://cdn.bootcss.com/bootstrap/3.3.6/css/bootstrap.min.css" rel="stylesheet"/>
  <style type="text/css">
   #xmain img {
                  max-width: 100%;
                  display: block;
                  margin-top: 10px;
                  margin-bottom: 10px;
                }

                #xmain p {
                    line-height:150%;
                    font-size: 16px;
                    margin-top: 20px;
                }

                #xmain h2 {
                    font-size: 24px;
                }

                #xmain h3 {
                    font-size: 20px;
                }

                #xmain h4 {
                    font-size: 18px;
                }


                .header {
	           background-color: #0099ff;
	           color: #ffffff;
	           margin-bottom: 20px;
	        }

	        .header p {
                  margin: 0px;
                  padding: 10px 0;
                  display: inline-block;  
                  vertical-align: middle;
                  font-size: 16px;
               }

               .header a {
                 color: white;
               }

              .header img {
                 height: 25px;
              }
  </style>
  <script src="http://cdn.bootcss.com/jquery/3.0.0/jquery.min.js">
  </script>
  <script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript">
   MathJax.Hub.Config({elements: ["bbpress-forums"]});
  </script>
  <script src="http://nautstatic-10007657.file.myqcloud.com/static/css/readability.min.js" type="text/javascript">
  </script>
  <script type="text/javascript">
   $(document).ready(function() {
                 var loc = document.location;
                 var uri = {
                  spec: "http://cos.name/cn/profile/103183/replies/page/14/",
                  host: "http://cos.name",
                  prePath: "http://cos.name",
                  scheme: "http",
                  pathBase: "http://cos.name/"
                 };
    
                 var documentClone = document.cloneNode(true);
                 var article = new Readability(uri, documentClone).parse();
     
                 document.getElementById("xmain").innerHTML = article.content;
                });
  </script>
  <!-- 1466460049: Accept with keywords: (title(0.0):论坛, topn(0.366666666667):大家,概率,方差,课件,帖子,互斥,陷阱,均匀,过程,函数,用户名,意义,被积,圆形,答案,圆筒,两题,密码,淋雨,楼主,C++,大学,总计,随机,版主,可加性,统计学,主题,数理统计,密度).-->
 </head>
 <body class="bbp-user-page single singular bbpress paged-14 single-author sidebar" onload="">
  <div class="header">
   <div class="container">
    <div class="row">
     <div class="col-xs-6 col-sm-6 text-left">
      <a href="/databee">
       <img src="http://nautidea-10007657.cos.myqcloud.com/logo_white.png"/>
      </a>
      <a href="/databee">
       <p>
        数螺
       </p>
      </a>
     </div>
     <div class="hidden-xs col-sm-6 text-right">
      <p>
       致力于数据科学的推广和知识传播
      </p>
     </div>
    </div>
   </div>
  </div>
  <div class="container text-center">
   <h1>
    easttiger的回复
   </h1>
  </div>
  <div class="container" id="xmain">
   <div class="hfeed site" id="page">
    <header class="site-header" id="masthead" role="banner">
     <div id="cos-logo">
      <a href="http://cos.name/cn">
       <img src="http://cos.name/cn/wp-content/themes/COS-forest/images/headers/cos-logo.png"/>
      </a>
     </div>
     <div class="navbar" id="navbar">
      <nav class="navigation main-navigation" id="site-navigation" role="navigation">
       <h3 class="menu-toggle">
        菜单
       </h3>
       <div class="menu-%e8%8f%9c%e5%8d%951-container">
        <ul class="nav-menu" id="menu-%e8%8f%9c%e5%8d%951">
         <li class="menu-item menu-item-type-custom menu-item-object-custom menu-item-home menu-item-407772" id="menu-item-407772">
          <a href="http://cos.name/cn/">
           论坛首页
          </a>
         </li>
         <li class="menu-item menu-item-type-custom menu-item-object-custom menu-item-407773" id="menu-item-407773">
          <a href="http://cos.name/cn/forums/">
           讨论区
          </a>
         </li>
         <li class="menu-item menu-item-type-custom menu-item-object-custom menu-item-407774" id="menu-item-407774">
          <a href="http://cos.name/cn/wp-login.php?action=register">
           注册
          </a>
         </li>
         <li class="menu-item menu-item-type-custom menu-item-object-custom menu-item-407819" id="menu-item-407819">
          <a href="http://cos.name/">
           主站
          </a>
         </li>
        </ul>
       </div>
      </nav>
      <!-- #site-navigation -->
     </div>
     <!-- #navbar -->
    </header>
    <!-- #masthead -->
    <div class="site-main" id="main">
     <div class="content-area" id="primary">
      <div class="site-content" id="content" role="main">
       <article class="post-0 type- status-publish hentry" id="post-0">
        <header class="entry-header">
         <h1 class="entry-title">
          easttiger
         </h1>
        </header>
        <!-- .entry-header -->
        <div class="entry-content">
         <div id="bbpress-forums">
          <div id="bbp-user-wrapper">
           <div id="bbp-single-user-details">
            <div id="bbp-user-avatar">
             <span class="vcard">
              <a class="url fn n" href="http://cos.name/cn/profile/103183/" rel="me" title="easttiger">
               <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=150&amp;d=monsterid&amp;r=g"/>
              </a>
             </span>
            </div>
            <!-- #author-avatar -->
            <div id="bbp-user-navigation">
             <ul>
              <li class="">
               <span class="vcard bbp-user-profile-link">
                <a class="url fn n" href="http://cos.name/cn/profile/103183/" rel="me" title="easttiger的档案">
                 档案
                </a>
               </span>
              </li>
              <li class="">
               <span class="bbp-user-topics-created-link">
                <a href="http://cos.name/cn/profile/103183/topics/" title="easttiger发起的主题">
                 发起的主题
                </a>
               </span>
              </li>
              <li class="current">
               <span class="bbp-user-replies-created-link">
                <a href="http://cos.name/cn/profile/103183/replies/" title="easttiger创建的回复">
                 创建的回复
                </a>
               </span>
              </li>
              <li class="">
               <span class="bbp-user-favorites-link">
                <a href="http://cos.name/cn/profile/103183/favorites/" title="easttiger的收藏夹">
                 收藏夹
                </a>
               </span>
              </li>
             </ul>
            </div>
            <!-- #bbp-user-navigation -->
           </div>
           <!-- #bbp-single-user-details -->
           <div id="bbp-user-body">
            <div class="bbp-user-replies-created" id="bbp-user-replies-created">
             <h2 class="entry-title">
              回复的主题
             </h2>
             <div class="bbp-user-section">
              <div class="bbp-pagination">
               <div class="bbp-pagination-count">
                查看 15 个帖子 - 196 到 210（总计 222 个）
               </div>
               <div class="bbp-pagination-links">
                <a class="prev page-numbers" href="http://cos.name/cn/profile/103183/replies/page/13/">
                 ←
                </a>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/">
                 1
                </a>
                <span class="page-numbers dots">
                 …
                </span>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/page/13/">
                 13
                </a>
                <span class="page-numbers current">
                 14
                </span>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/page/15/">
                 15
                </a>
                <a class="next page-numbers" href="http://cos.name/cn/profile/103183/replies/page/15/">
                 →
                </a>
               </div>
              </div>
              <ul class="forums bbp-replies" id="topic-0-replies">
               <li class="bbp-header">
                <div class="bbp-reply-author">
                 作者
                </div>
                <!-- .bbp-reply-author -->
                <div class="bbp-reply-content">
                 帖子
                </div>
                <!-- .bbp-reply-content -->
               </li>
               <!-- .bbp-header -->
               <li class="bbp-body">
                <div class="bbp-reply-header" id="post-281622">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年12月14日 下午4:32
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17565/">
                    关于数学期望与方差的关系
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17565/#post-281622">
                   13 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-281622 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-17565 bbp-reply-position-13 user-id-103183 post-281622 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   1. 这里存在的意思绝对值是小于无穷大
                   <br/>
                   2. 只要看到期望和方差都是更高层意义下的积分就可以了. 只不过初学时积分是假设x轴均匀"密度", 但积分并不一定更需要x轴均匀"密度", 可以是不均匀密度. 直观上期望就可以理解为这样一种x轴密度不均匀的积分, 密度函数就是pdf, 而3楼式子中提到的dP就是f(x)与dx的乘积, 可以看成是一段"质量元". 期望的被积函数是x, 方差稍微变一下其实就是以x^2为主要成分的被积函数.
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-281618">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年12月14日 下午3:51
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17106/">
                    数学笔记1 度量空间
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17106/#post-281618">
                   2 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-281618 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-17106 bbp-reply-position-2 user-id-103183 topic-author post-281618 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   开始一天更新一点, 争取2009年能写掉这页
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-280318">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月12日 上午11:21
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17194/">
                    数理统计学习问题
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17194/#post-280318">
                   4 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-280318 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-17194 bbp-reply-position-4 user-id-103183 post-280318 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   hehe, 我还在念本科,不过以后想做统计计算方面的研究
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-280251">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月11日 下午1:56
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17194/">
                    数理统计学习问题
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17194/#post-280251">
                   2 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-280251 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-17194 bbp-reply-position-2 user-id-103183 post-280251 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   在R和统计上我都是个新手, 但我之前有段时间也和楼主有样的观点, 不过现在觉得R正是介乎C++和MATLAB之间的那个角色.  所以就来说说自己的看法.
                   <br/>
                   我以前也喜欢C++是因为觉得它没有任何框架, 什么东西只要想要, 就能写. 但坏处是要写的东西太多, 对统计的支持不够, 或者说用C++的统计人相对来说不够多. MATLAB功能很丰富, 但是再丰富也不可能全面, 许多时候为了一些小事却办不到. 当然一定要做是可以的, 但是得深入到MATLAB语言基本层面去学"编程", 而不是在外部学怎么"使用", 但要学深入就发现资料很难找, 而且作为公司来说为了做标准化应该也不希望太多人了解得很深. 所以R在这方面就弥补了两者的劣势, R既具有一门普通编程语言的可塑性, 又有许多现成封装的函数库可以用.
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-280167">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月9日 下午5:15
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/7653/">
                    我在火车上上厕所的尴尬经历
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/7653/page/8/#post-280167">
                   119 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-280167 -->
                <div class="odd bbp-parent-forum-1001 bbp-parent-topic-7653 bbp-reply-position-119 user-id-103183 post-280167 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   cccccccccccccccc
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-280166">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月9日 下午5:15
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/10541/">
                    震撼,绝对震撼,小学生都如此,我们呢?
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/10541/page/6/#post-280166">
                   77 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-280166 -->
                <div class="even bbp-parent-forum-1001 bbp-parent-topic-10541 bbp-reply-position-77 user-id-103183 post-280166 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   cccccccccc
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-280090">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月7日 下午4:26
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17111/">
                    stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17111/#post-280090">
                   4 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-280090 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-17111 bbp-reply-position-4 user-id-103183 post-280090 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <blockquote class="d4pbbc-quote">
                   <p>
                    引用楼主hanshua于2009-11-04 09:26发表的 stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论 :
                    <br/>
                    5. I have 4 umbrellas, some at home, some in the office. I keep moving between home and office. I take an umbrella with me only if it rains. If it does not rain I leave the umbrella behind (at home or in the office). It may happen that all umbrellas are in one place, I am at the other, it starts raining and must leave, so I get wet.
                    <br/>
                    1. If the probability of rain is p, what is the probability that I get wet?
                    <br/>
                    2. Current estimates show that p = 0.6 in Edinburgh. How many umbrellas should I have so that, if I follow the strategy above, the probability I get wet is less than 0.1?
                   </p>
                  </blockquote>
                  <p>
                   有点不清楚那个p到底是瞬时下雨概率还是时段(比如一天中)下雨概率.
                   <br/>
                   姑且当瞬时下雨概率
                   <br/>
                   则写出transition probability matrix: (以家中存雨伞数{0,1,2,3,4}为state space)
                   <br/>
                   A =
                   <br/>
                   [         1-p,           p,                       0,                    0,                      0
                   <br/>
                   p*(1-p),   p^2+(1-p)^2,     p*(1-p),               0,                      0
                   <br/>
                   0,           p*(1-p),       p^2+(1-p)^2,     p*(1-p),                0
                   <br/>
                   0,             0,                   p*(1-p),           p^2+(1-p)^2,     p*(1-p)
                   <br/>
                   0,             0,                        0,                p*(1-p),          1-p*(1-p)        ]
                  </p>
                  <p>
                   设极限概率为[a,b,c,d,e]
                   <br/>
                   那么由对称性知b=c=d=e
                   <br/>
                   只要解a和b关系即可 (5个极限概率之和=1)
                   <br/>
                   由第一列: a*(1-p) + b*p*(1-p) = a
                   <br/>
                   可最后解得 a = (1-p)/(5-p),  b = 1/(5-p)       比如当p=0.6,  a=1/11,  b = 5/22
                  </p>
                  <p>
                   淋雨的平均意义上的概率因为 家中无伞时出门下雨 + 全部伞都在家但离家时没下雨而从办公室回来时下雨 = a*p + e*(1-p)*p = 2p(1-p)/(5-p)
                   <br/>
                   这样的话p=0.6时他从平均意义上淋到雨的概率为6/55 (&gt;6/60)
                  </p>
                  <p>
                   实际上假设有N把伞, a = (1-p)/(N+1-p),  b=1/(N+1-p)
                   <br/>
                   于是淋雨概率变成 2p(1-p)/(N+1-p)
                   <br/>
                   当p=0.6, 淋雨概率为0.48/(N+0.4) &lt; 0.1 =&gt; N &gt;4.4 =&gt; N至少为5
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279980">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月5日 上午7:01
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17111/">
                    stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17111/#post-279980">
                   3 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279980 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-17111 bbp-reply-position-3 user-id-103183 post-279980 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <blockquote class="d4pbbc-quote">
                   <p>
                    引用楼主hanshua于2009-11-04 09:26发表的 stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论 :
                    <br/>
                    3. A certain calculating machineuses only the digits 0 and 1. It is supposed to transmit one of thesedigits through several stages. However, at every stage, there is aprobability p that the digit that enters this stage will be changedwhen it leaves and a probability q = 1 − p that it won’t. Form a Markovchain to represent the process of transmission by taking as states thedigits 0 and 1.
                   </p>
                   <p>
                    What is the matrix of transitionprobabilities? Now draw a tree and assign probabilities assuming thatthe process begins in state 0 and moves through two stages oftransmission. What is the probability that the machine, after twostages, produces the digit 0 (i.e., the correct digit)?
                   </p>
                  </blockquote>
                  <p>
                   Transition probability matrix:
                   <br/>
                   P =
                   <br/>
                   (0)   (1)
                   <br/>
                   (0)  [    q      p
                   <br/>
                   (1)       p      q     ]
                  </p>
                  <p>
                   tree:
                   <br/>
                   <img src="http://web.hku.hk/%7Ejdong/img/_0002.png"/>
                  </p>
                  <p>
                   P^2 =
                   <br/>
                   [   p^2+q^2            2pq
                   <br/>
                   2pq              p^2+q^2   ]
                  </p>
                  <p>
                   The probability of producing 0 after two stages is p^2+q^2.
                  </p>
                  <blockquote class="d4pbbc-quote">
                   <p>
                    引用楼主hanshua于2009-11-04 09:26发表的 stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论 :
                    <br/>
                    4. Assume that a man’s professioncan be classified as professional, skilled labourer, or unskilledlabourer. Assume that, of the sons of professional men, 80 percent areprofessional, 10 percent are skilled labourers, and 10 percent areunskilled labourers. In the case of sons of skilled labourers, 60percent are skilled labourers, 20 percent are professional, and 20percent are unskilled. Finally, in the case of unskilled labourers, 50percent of the sons are unskilled labourers, and 25 percent each are inthe other two categories. Assume that every man has at least one son,and form a Markov chain by following the profession of a randomlychosen son of a given family through several generations. Set up thematrix of transition probabilities. Find the probability that arandomly chosen grandson of an unskilled labourer is a professional man.
                   </p>
                  </blockquote>
                  <p>
                   Transition probability matrix:
                   <br/>
                   A =
                   <br/>
                   (P)            (S)           (U)
                   <br/>
                   (P) [   0.8000    0.1000    0.1000
                   <br/>
                   (S)     0.2000    0.6000    0.2000
                   <br/>
                   (U)     0.2500    0.2500    0.5000  ]
                  </p>
                  <p>
                   A^2 =
                   <br/>
                   [   0.6850    0.1650    0.1500
                   <br/>
                   0.3300    0.4300    0.2400
                   <br/>
                   0.3750    0.3000    0.3250  ]
                   <br/>
                   So the probability that a randomly chosen grandson of an unskilled labourer is a professional man is 0.375
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279934">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月4日 上午8:12
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17111/">
                    stochastic processes 随机过程 每天更新两题，次日公布答案，欢迎大家踊跃讨论
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17111/#post-279934">
                   2 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279934 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-17111 bbp-reply-position-2 user-id-103183 post-279934 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   Let me try.
                  </p>
                  <p>
                   1. (i) Transition probability is
                   <br/>
                   A =
                   <br/>
                   [   0.8000    0.2000         0
                   <br/>
                   0.3000    0.4000    0.3000
                   <br/>
                   0.2000    0.1000    0.7000  ]
                  </p>
                  <p>
                   A^2 =
                   <br/>
                   [   0.7000    0.2400    0.0600
                   <br/>
                   0.4200    0.2500    0.3300
                   <br/>
                   0.3300    0.1500    0.5200  ]
                  </p>
                  <p>
                   So given it is a grandson of a Harvard graduate, Probability of his going to Harvard is 0.7
                  </p>
                  <p>
                   (ii) Now the first row of the transition matrix has been changed to [1 0 0], therefore the the first row of A^2 will be [1 0 0]. That will modify the demanded probability to 1.
                  </p>
                  <p>
                   2(i)
                   <br/>
                   Transition matrix is
                   <br/>
                   G =
                   <br/>
                   [   0.5000    0.5000         0
                   <br/>
                   0.2500    0.5000    0.2500
                   <br/>
                   0         0.5000    0.5000         ]
                   <br/>
                   (ii) It's easy to prove the second row of G^n will always be [0.25, 0.5, 0.25]. This shall correspond to the probabilities asked. They don't change for different n's.
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279820">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年11月1日 上午3:51
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/16916/">
                    求助一个统计学的基本原理！
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/16916/#post-279820">
                   7 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279820 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-16916 bbp-reply-position-7 user-id-103183 post-279820 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <blockquote class="d4pbbc-quote">
                   <p>
                    引用第4楼xjuchenwei于2009-10-22 22:41发表的 :
                    <br/>
                    这个就是概率中的半可加性呀，P(A1∪…∪An)&lt;=∑P(Ai)  i=1,…,n
                   </p>
                  </blockquote>
                  <p>
                   补充4楼:
                  </p>
                  <p>
                   且n可取正无穷.
                  </p>
                  <p>
                   但这个可能不叫半可加性. 而只是概率的可列可加性+非负性的一个结果.
                  </p>
                  <p>
                   可列可加性说如果A1,A2,…两两互斥, 则上式变成等式.
                  </p>
                  <p>
                   一般来说半可加性说即使两两互斥, 上式还是可以维持小于等于的形式.
                  </p>
                  <p>
                   当然A1,A2,…不一定两两互斥, 于是把他们的并写成若干互斥的集合的并时要去掉它们非空的交, 这些非空的交集的概率须非负, 从而有了小于等于号.
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279809">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年10月31日 下午10:21
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/15581/">
                    R study notes 3 – More complicated (and powerful) Objects and Data structures
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/15581/#post-279809">
                   3 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279809 -->
                <div class="odd bbp-parent-forum-999 bbp-parent-topic-15581 bbp-reply-position-3 user-id-103183 topic-author post-279809 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   hehe, 最近一直再用matlab, R倒有点生疏了. 等matlab的事告一段落, 就要用R写一个project, 那时侯来补
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279701">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年10月29日 下午5:54
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17041/">
                    帮忙翻译两句话
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17041/#post-279701">
                   2 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279701 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-17041 bbp-reply-position-2 user-id-103183 post-279701 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   感觉两个皆有可能, 视乎具体simulation的细节而定.
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279617">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年10月28日 上午7:48
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/13764/">
                    英国著名大学布里斯托大学部分统计课程课件
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/13764/page/16/#post-279617">
                   238 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279617 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-13764 bbp-reply-position-238 user-id-103183 post-279617 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   ccccccccccccccccccccccccc
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279609">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年10月28日 上午5:30
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/14470/">
                    世界著名大学牛津大学统计学部分讲义及课件
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/14470/page/13/#post-279609">
                   187 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279609 -->
                <div class="even bbp-parent-forum-991 bbp-parent-topic-14470 bbp-reply-position-187 user-id-103183 post-279609 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   ccccccccccccccccccc
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
                <div class="bbp-reply-header" id="post-279601">
                 <div class="bbp-meta">
                  <span class="bbp-reply-post-date">
                   2009年10月28日 上午3:57
                  </span>
                  <span class="bbp-header">
                   回复：
                   <a class="bbp-topic-permalink" href="http://cos.name/cn/topic/17008/">
                    一个概率论的问题
                   </a>
                  </span>
                  <a class="bbp-reply-permalink" href="http://cos.name/cn/topic/17008/#post-279601">
                   2 楼
                  </a>
                  <span class="bbp-admin-links">
                  </span>
                 </div>
                 <!-- .bbp-meta -->
                </div>
                <!-- #post-279601 -->
                <div class="odd bbp-parent-forum-991 bbp-parent-topic-17008 bbp-reply-position-2 user-id-103183 post-279601 reply type-reply status-publish hentry">
                 <div class="bbp-reply-author">
                  <a class="bbp-author-avatar" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   <img src="http://sdn.geekzu.org/avatar/abaead86be3dc59380199f1e9e35c5bb?s=80&amp;d=monsterid&amp;r=g"/>
                  </a>
                  <br/>
                  <a class="bbp-author-name" href="http://cos.name/cn/profile/103183/" rel="nofollow" title="查看easttiger的档案">
                   easttiger
                  </a>
                  <br/>
                  <div class="bbp-author-role">
                   版主
                  </div>
                 </div>
                 <!-- .bbp-reply-author -->
                 <div class="bbp-reply-content">
                  <p>
                   能具体点吗?比如容器是个圆形面还是圆筒, 陷阱是分布在圆形面上的还是圆筒内壁上. 是有K个陷阱吗?
                  </p>
                 </div>
                 <!-- .bbp-reply-content -->
                </div>
                <!-- .reply -->
               </li>
               <!-- .bbp-body -->
               <li class="bbp-footer">
                <div class="bbp-reply-author">
                 作者
                </div>
                <div class="bbp-reply-content">
                 帖子
                </div>
                <!-- .bbp-reply-content -->
               </li>
               <!-- .bbp-footer -->
              </ul>
              <!-- #topic-0-replies -->
              <div class="bbp-pagination">
               <div class="bbp-pagination-count">
                查看 15 个帖子 - 196 到 210（总计 222 个）
               </div>
               <div class="bbp-pagination-links">
                <a class="prev page-numbers" href="http://cos.name/cn/profile/103183/replies/page/13/">
                 ←
                </a>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/">
                 1
                </a>
                <span class="page-numbers dots">
                 …
                </span>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/page/13/">
                 13
                </a>
                <span class="page-numbers current">
                 14
                </span>
                <a class="page-numbers" href="http://cos.name/cn/profile/103183/replies/page/15/">
                 15
                </a>
                <a class="next page-numbers" href="http://cos.name/cn/profile/103183/replies/page/15/">
                 →
                </a>
               </div>
              </div>
             </div>
            </div>
            <!-- #bbp-user-replies-created -->
           </div>
          </div>
         </div>
        </div>
        <!-- .entry-content -->
        <footer class="entry-meta">
        </footer>
        <!-- .entry-meta -->
       </article>
       <!-- #post -->
      </div>
      <!-- #content -->
     </div>
     <!-- #primary -->
     <div class="sidebar-container" id="tertiary" role="complementary">
      <div class="sidebar-inner">
       <div class="widget-area">
        <aside class="widget bbp_widget_login" id="bbp_login_widget-2">
         <h3 class="widget-title">
          登录
         </h3>
         <form action="http://cos.name/cn/wp-login.php" class="bbp-login-form" method="post">
          <fieldset>
           <legend>
            登录
           </legend>
           <div class="bbp-username">
            <label for="user_login">
             用户名:
            </label>
           </div>
           <div class="bbp-password">
            <label for="user_pass">
             密码:
            </label>
           </div>
           <div class="bbp-remember-me">
            <label for="rememberme">
             记住用户名
            </label>
           </div>
           <div class="bbp-submit-wrapper">
            <button class="button submit user-submit" id="user-submit" name="user-submit" tabindex="104" type="submit">
             登录
            </button>
           </div>
           <div class="bbp-login-links">
            <a class="bbp-register-link" href="http://cos.name/cn/wp-login.php?action=register" title="注册">
             注册
            </a>
            <a class="bbp-lostpass-link" href="http://cos.name/cn/wp-login.php?action=lostpassword" title="忘记密码">
             忘记密码
            </a>
           </div>
          </fieldset>
         </form>
        </aside>
        <aside class="widget widget_text" id="text-7">
         <h3 class="widget-title">
          搜索
         </h3>
         <div class="textwidget">
          <form action="http://www.google.com/search" id="bbp-search-form" method="get" onsubmit="Gsitesearch(this)" role="search">
           <div>
           </div>
          </form>
          <form id="bbp-search-form-baidu" onsubmit="g(this)" role="search">
           <div>
           </div>
          </form>
         </div>
        </aside>
        <aside class="widget widget_text" id="text-2">
         <h3 class="widget-title">
          新鲜事
         </h3>
         <div class="textwidget">
          <ul>
           <li>
            <a href="http://cos.name/cn/topics/">
             最新帖子
            </a>
           </li>
           <li>
            <a href="http://cos.name/cn/view/popular/">
             最热门主题
            </a>
           </li>
           <li>
            <a href="http://cos.name/cn/view/no-replies/">
             消灭零回复
            </a>
           </li>
          </ul>
         </div>
        </aside>
        <aside class="widget widget_text" id="text-3">
         <h3 class="widget-title">
          RSS订阅
         </h3>
         <div class="textwidget">
          <ul>
           <li>
            <img src="http://cos.name/wp-includes/images/rss.png"/>
            <a href="http://cos.name/cn/topics/feed/">
             所有主题
            </a>
           </li>
           <li>
            <img src="http://cos.name/wp-includes/images/rss.png"/>
            <a href="http://cos.name/cn/forums/feed/">
             所有帖子
            </a>
           </li>
          </ul>
         </div>
        </aside>
       </div>
       <!-- .widget-area -->
      </div>
      <!-- .sidebar-inner -->
     </div>
     <!-- #tertiary -->
    </div>
    <!-- #main -->
    <footer class="site-footer" id="colophon" role="contentinfo">
     <div class="site-info">
      版权所有 © 2014 统计之都 | 由
      <a href="http://wordpress.org/">
       WordPress
      </a>
      构建 | 主题修改自
      <a href="http://wordpress.org/themes/twentythirteen">
       Twenty Thirteen
      </a>
     </div>
     <!-- .site-info -->
    </footer>
    <!-- #colophon -->
   </div>
   <!-- #page -->
  </div>
 </body>
</html>